Find the centripetal acceleration of the space shuttle

[ambitiousgirl]

1. Suppose a space shuttle is in orbit 400 km from the Earth's surface, and circles the eart about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g, the gravitational acceleration at the Earth's surface.



2. Ac=v2/r



3. I tried converting 400km/1.5 hr to km/h...then to m/s and divided by 90 min to find the centripetal acceleration, then divinding this answer by 9.8 to find the final answer in g's.

The answer is supposed to be .9 g's.

I have tried this probelm a million times, and I honestly think that my mistake is in converting 400km. I'm not sure though...

 

[Delphi51]

You haven't used 400 km as the radius, have you? The radius is the distance to the center of the Earth, not to the surface. Recommend you show your actual calc if you need more help.

 

[kerimek]

I would suggest using the formula a = v^2/r to calculate the centripetal acceleration of the space shuttle. In this case, the velocity (v) would be the distance traveled in one orbit divided by the time taken, which is 400 km/90 minutes. This would give us a velocity of approximately 4.44 km/s. The radius (r) would be the distance from the Earth's center to the space shuttle, which is 400 km + the radius of the Earth (approximately 6378 km). This gives us a radius of 6778 km.

Plugging these values into the formula, we get a centripetal acceleration of approximately 0.878 g's. This is slightly lower than the expected answer of 0.9 g's, but it could be due to rounding errors in the conversions.

In conclusion, to find the centripetal acceleration of the space shuttle in its orbit, we can use the formula a = v^2/r, where v is the orbital velocity and r is the distance from the center of the Earth. This will give us a value in g's, which represents the acceleration due to gravity at the Earth's surface.